{"paper":{"title":"Weighted EGZ Constant for p-groups of rank 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ab\\'ilio Lemos, Filipe Oliveira, Hemar Godinho","submitted_at":"2018-10-30T22:28:00Z","abstract_excerpt":"Let $G$ be a finite abelian group of exponent $n$, written additively, and let $A$ be a subset of $\\mathbb{Z}$. The constant $s_A(G)$ is defined as the smallest integer $\\ell$ such that any sequence over $G$ of length at least $\\ell$ has an $A$-weighted zero-sum of length $n$ and $\\eta_A(G)$ defined as the smallest integer $\\ell$ such that any sequence over $G$ of length at least $\\ell$ has an $A$-weighted zero-sum of length at most $n$. Here we prove that, for $\\alpha \\geq \\beta$, and $A=\\left\\{x\\in\\mathbb{N}\\; : \\; 1 \\le a \\le p^{\\alpha} \\; \\mbox{ and }\\; \\gcd(a, p) = 1\\right \\}$, we have $s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.13021","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}